Does strong repulsion lead to smooth solutions in a repulsion-attraction chemotaxis system even when starting with highly irregular initial data?

It has been well established that, in attraction-repulsion Keller–Segel systems of the form$ \begin{equation*} \left\{ \begin{aligned} u_t & = \Delta u - \chi \nabla \cdot (u\nabla v) + \xi w), \\ \tau v_t v \alpha \beta v, w_t w \gamma \delta \end{aligned} \right. \end{equation*} $in a smooth bounded domain $ \Omega \subseteq \mathbb{R}^n $, n\in\mathbb{N} with Neumann boundary conditions and parameters \chi, \geq 0 \alpha, \beta, \gamma, > \in \{0, 1\} finite-time blow-up can be ruled out many scenarios given sufficiently initial data if repulsive chemotaxis is stronger than its attractive counterpart. In this paper, we will go sense step further by studying same system that could already understood as being blown-up state (e.g. positive Radon measure for first solution component) then ask question whether strong repulsion enough regularizing effect to lead existence solution, which still connected said sensible fashion. Regarding this, fact establish construction such possible two-dimensional parabolic-parabolic two- three-dimensional parabolic-elliptic under appropriate assumptions on interaction attraction data.